PERBANDINGAN METODE MAXIMUM LIKELIHOOD DAN METODE BAYES DALAM MENGESTIMASI PARAMETER MODEL REGRESI LINIER BERGANDA UNTUK DATA BERDISTRIBUSI NORMAL

Authors

  • Catrin Muharisa
  • Ferra Yanuar
  • Hazmira Yozza

DOI:

https://doi.org/10.25077/jmu.4.2.100-107.2015

Abstract

Analisis regresi merupakan salah satu metode untuk melihat hubungan antara variabel bebas (independent) dengan variabel terikat (dependent) yang dinyatakan dalam model regresi. Beberapa metode yang bisa digunakan untuk mengestimasi parameter model regresi, diantaranya adalah metode klasik dan metode Bayes. Salah satu metode klasik adalah metode maximum likelihood. Penelitian ini membahas tentang perbandingan metode maximum likelihood dan metode Bayes dalam mengestimasi parameter model regresi linear berganda untuk data berdistribusi normal. Adapun rumus untuk mengestimasi parameter dengan metode maximum likelihood adalah βˆ=(XTX)-1XTY dan ˆσ2 = 1 n P∞ k=1 ei. Sedangkan untuk mengestimasi parameter dengan metode Bayes adalah dengan menggunakan distribusi prior dan fungsi likelihood. Distribusi prior yag dipilih pada kajian ini adalah f(β, σ2 ) = Qn i=1 f(βj |σ 2 )f(σ 2 ) dengan βj ∼ N(µβj , σ2 ) dan σ 2 ∼ IG(a, b). Distribusi prior konjugat tersebut kemudian dikalikan dengan fungsi likelihood L(β, σ2 ) sehingga membentuk distribusi posterior f(β|σ 2 ). Distribusi posterior inilah yang digunakan untuk mengestimasi parameter model melalui proses Markov Chain Monte Carlo (MCMC). Algoritma MCMC yang digunakan adalah algoritma Gibbs Sampler. Model regresi linear berganda yang diperoleh dengan metode maximum likelihood adalah

yˆ = −27, 8210000 + 0, 0307430X1 + 0, 0039211X2 + 0, 0034631X3 + 0, 6537000X4

dengan kecocokan modelnya adalah sebesar 95,7 %. Sedangkan model regresi linear berganda yang diperoleh dengan metode Bayes adalah

yˆ = −26, 620000 + 0, 029380X1 + 0, 004204X2 + 0, 003321X3 + 0, 656200X4

dengan kecocokan modelnya adalah sebesar 99,99 %. Dengan demikian dapat disimpulkan bahwa metode Bayes lebih baik dari pada metode maximum likelihood.

Kata Kunci: Model Regresi Linear Berganda, metode Maximum Likelihood, dan metode Bayes

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Published

26-07-2019

Issue

Vol. 4 No. 2 (2015)

Section

Articles

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